The Hopf-Fibration and HiddenVariables in Quantum and ClassicalMechanics

Brian O’Sullivan has rewritten his latest article about having quaternions as hidden variables for a particle and thereby explaining several of the phenomena observed in the quantum reign.

He also proposes an experiment to verify whether his theory is correct, using 3 Stern-Gerlach apparatus in series. 

Although his final conclusions have a bit weakened in comparison to his earlier version (see my previous post), the remain is still very interesting:

In light of the fact that the Quantum theory has not recognized that the qubit is a unit quaternion, we conclude that Quantum Mechanics is not only incomplete but observably inadequate as there are indeed hidden variables unaccounted for by the theory. These hidden variables are found in the parameter space of the spinor.

As written before his ideas very much align with those from Joy Christian, but he has not yet accounted for probably the most profound 'proof of entanglement' in QM, being the EPR-Bell experiment. I am looking forward to see more from this author.

Add 2016/12/10: I have updated the link to the article below, as the former didn't work anymore.

1.  The Hopf-Fibration and HiddenVariables in Quantum and ClassicalMechanics, http://www.meditations-on-geometry.net/s/Meditations-On-Geometry1stMeditation.pdf
2. Brian O’Sullivan website: http://www.meditations-on-geometry.net/

Independent Confirmation of Joy Christian’s Model

Last week a young physicist from Ireland, Brian O'Sullivan, published an article(1) in which he arrives at the same conclusion as Joy Christian that the hidden variable that is responsible for the spin related behavior of fundamental particles, is based on the constraints of the surface of a 4-dimensional sphere (S3).

While Brian's approach is quite different (for example he uses the quaternion representation of the spin, while Joy tends to use bivectors and Geometric Algebra) both physicists state that the particular quantum behavior is caused by the hopf-vibration between the S3 and the S2 space.

His conclusions are as remarkable as those of Joy Christian:

The parameter space of the quaternion accounts for the statistics of all the fundamental particles, integer and half-integer, in a natural way, and most importantly it does so deterministically.
The theory of the fundamental particles formed from Hamilton's quaternions is a deterministic local Hidden Variable theory.

and

With no superposition, there is no decoherence, and it follows that Quantum Information is a fundamentally flawed science, and the reason that Quantum Computing has not been achieved to date is that it will never be achieved ...

Brian has not referenced the work of Joy Christian. This, and the fact that his approach is quite different, makes it reasonable to believe that he has made his case and conclusions independently from those of Joy Christian.

EDIT 26/06/2016: The author has temporary retracted his article: "Withdrawn due to the lack of sensitivity regarding the consequences of the presented results"

1. The Hopf-Fibration and Hidden Variables in Quantum and Classical Mechanics, Brian O'Sullivan, June 14, 2016, http://arxiv.org/pdf/1601.02569.pdf

Double slit is no longer proof of non-classical quantum behaviour!

Today it struck me again that the more then 50 years old position from Feynman about the double slit experiment:

"is impossible, absolutely impossible, to explain in any classical way" (1)

is still presented as being true in modern scientific and popular publications (2,5). In an earlier post I have already briefly discussed the experiments by Ives Couder (3), where he can mimic many quantum-like behaviors using macroscopic 'walkers' - tiny droplets bouncing on an silicon oil bath -, including the effects found for the double slit experiment.

Gerhard Grössing, from the Austrian Institute for Nonlinear Studies, has since then be working on simulating these pure classical behaviors. The most relevant publication in this context might be (4), where he summarizes:

"Despite claims in the literature that this scenario is to
be described by a dynamical nonlocality that could best be understood in the framework of the
Heisenberg picture, we show that an explanation can be cast within the framework of the
intuitively appealing Schrödinger picture as well"

The simulation (using individual particles at a time) reveals beautifully the interference bands of the dual split:

Within they're framework they explain how particles going individually through one of the slits can 'feel' whether or not the other slit is open or not. This is the paradox  Feynman stumbled over.

1. Feynman, R.P., Leighton, R.B., and Sands, M. (1965). The Feynman Lectures in Physics Volume 3, Section 1–1, Addison–Wesleyhttp://www.sci.buu.ac.th/~physics/chainarong/fundamental%20physics/Richard%20Feynman%20-%20The%20Feynman%20Lectures%20on%20Physics%20Volume%203.pdf
2. Quantum interference experiments, modular variables and weak measurements,Tollaksen et al, 2008, http://iopscience.iop.org/article/10.1088/1367-2630/12/1/013023/pdf
3. Single-Particle Diffraction andInterference ata Macroscopic Scale , Yves Couder, 2006,https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf
4. “Systemic Nonlocality” from Changing Constraints on
   Sub-Quantum Kinematics, Grössing et al, 2013,  http://arxiv.org/pdf/1303.2867v1.pdf
5. Life on the Edge: The Coming of Age of Quantum Biology (2014), Jim Al-Khalili et al., https://66853306a5a50e53d218b618b57187c98158872c.googledrive.com/host/0B2zRsOz7CYloZjV6aURDc1daWjQ/hasil_29/0307986810-Life-Edge-Coming-Quantum-Biology.pdf